Boyle's Law Calculator
Calculate pressure or volume changes using Boyle's Law (P1×V1 = P2×V2).
Find any missing variable.
Boyle’s Law describes the inverse relationship between the pressure and volume of a gas at constant temperature. First published by Robert Boyle in 1662, it was one of the earliest quantitative physical laws and forms the foundation of modern gas theory.
The formula: P₁V₁ = P₂V₂
Where:
- P₁ = initial pressure (any consistent unit: atm, kPa, mmHg, psi)
- V₁ = initial volume (any consistent unit: L, mL, m³, ft³)
- P₂ = final pressure
- V₂ = final volume
This relationship holds only when temperature (T) and amount of gas (n) remain constant. The product P × V always equals a constant k for a given gas sample at fixed temperature: PV = k
Rearranged forms:
- Solving for final volume: V₂ = P₁V₁ / P₂
- Solving for final pressure: P₂ = P₁V₁ / V₂
Physical intuition: Compressing a gas into a smaller space forces molecules closer together, increasing collision frequency with container walls — which is pressure. Double the pressure → half the volume. Halve the pressure → double the volume.
Worked example: A gas occupies 8.0 L at a pressure of 1.5 atm. The pressure is increased to 3.0 atm at constant temperature. What is the new volume?
V₂ = P₁V₁ / P₂ = (1.5 × 8.0) / 3.0 = 12.0 / 3.0 = 4.0 L
The volume halved when pressure doubled — exactly as Boyle’s Law predicts.
Real-world applications: scuba diving (gas volume in tanks vs. depth pressure), bicycle pumps (compressing air increases pressure), syringes (pulling the plunger expands volume and draws in fluid), and industrial gas compression systems.
Limitation: Boyle’s Law applies to ideal gases. Real gases deviate at very high pressures or very low temperatures where intermolecular forces become significant.